/*
 * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
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 *
 *
 *
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 *
 *
 *
 *
 */

package java.lang;

import java.lang.annotation.Native;

/**
 * The {@code Integer} class wraps a value of the primitive type
 * {@code int} in an object. An object of type {@code Integer}
 * contains a single field whose type is {@code int}.
 *
 * <p>In addition, this class provides several methods for converting
 * an {@code int} to a {@code String} and a {@code String} to an
 * {@code int}, as well as other constants and methods useful when
 * dealing with an {@code int}.
 *
 * <p>Implementation note: The implementations of the "bit twiddling"
 * methods (such as {@link #highestOneBit(int) highestOneBit} and
 * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}) are
 * based on material from Henry S. Warren, Jr.'s <i>Hacker's
 * Delight</i>, (Addison Wesley, 2002).
 *
 * @author Lee Boynton
 * @author Arthur van Hoff
 * @author Josh Bloch
 * @author Joseph D. Darcy
 * @since JDK1.0
 */
public final class Integer extends Number implements Comparable<Integer> {

  /**
   * A constant holding the minimum value an {@code int} can
   * have, -2<sup>31</sup>.
   */
  @Native
  public static final int MIN_VALUE = 0x80000000;

  /**
   * A constant holding the maximum value an {@code int} can
   * have, 2<sup>31</sup>-1.
   */
  @Native
  public static final int MAX_VALUE = 0x7fffffff;

  /**
   * The {@code Class} instance representing the primitive type
   * {@code int}.
   *
   * @since JDK1.1
   */
  @SuppressWarnings("unchecked")
  public static final Class<Integer> TYPE = (Class<Integer>) Class.getPrimitiveClass("int");

  /**
   * All possible chars for representing a number as a String
   */
  final static char[] digits = {
      '0', '1', '2', '3', '4', '5',
      '6', '7', '8', '9', 'a', 'b',
      'c', 'd', 'e', 'f', 'g', 'h',
      'i', 'j', 'k', 'l', 'm', 'n',
      'o', 'p', 'q', 'r', 's', 't',
      'u', 'v', 'w', 'x', 'y', 'z'
  };

  /**
   * Returns a string representation of the first argument in the
   * radix specified by the second argument.
   *
   * <p>If the radix is smaller than {@code Character.MIN_RADIX}
   * or larger than {@code Character.MAX_RADIX}, then the radix
   * {@code 10} is used instead.
   *
   * <p>If the first argument is negative, the first element of the
   * result is the ASCII minus character {@code '-'}
   * ({@code '\u005Cu002D'}). If the first argument is not
   * negative, no sign character appears in the result.
   *
   * <p>The remaining characters of the result represent the magnitude
   * of the first argument. If the magnitude is zero, it is
   * represented by a single zero character {@code '0'}
   * ({@code '\u005Cu0030'}); otherwise, the first character of
   * the representation of the magnitude will not be the zero
   * character.  The following ASCII characters are used as digits:
   *
   * <blockquote>
   * {@code 0123456789abcdefghijklmnopqrstuvwxyz}
   * </blockquote>
   *
   * These are {@code '\u005Cu0030'} through
   * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
   * {@code '\u005Cu007A'}. If {@code radix} is
   * <var>N</var>, then the first <var>N</var> of these characters
   * are used as radix-<var>N</var> digits in the order shown. Thus,
   * the digits for hexadecimal (radix 16) are
   * {@code 0123456789abcdef}. If uppercase letters are
   * desired, the {@link java.lang.String#toUpperCase()} method may
   * be called on the result:
   *
   * <blockquote>
   * {@code Integer.toString(n, 16).toUpperCase()}
   * </blockquote>
   *
   * @param i an integer to be converted to a string.
   * @param radix the radix to use in the string representation.
   * @return a string representation of the argument in the specified radix.
   * @see java.lang.Character#MAX_RADIX
   * @see java.lang.Character#MIN_RADIX
   */
  public static String toString(int i, int radix) {
    if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX) {
      radix = 10;
    }

        /* Use the faster version */
    if (radix == 10) {
      return toString(i);
    }

    char buf[] = new char[33];
    boolean negative = (i < 0);
    int charPos = 32;

    if (!negative) {
      i = -i;
    }

    while (i <= -radix) {
      buf[charPos--] = digits[-(i % radix)];
      i = i / radix;
    }
    buf[charPos] = digits[-i];

    if (negative) {
      buf[--charPos] = '-';
    }

    return new String(buf, charPos, (33 - charPos));
  }

  /**
   * Returns a string representation of the first argument as an
   * unsigned integer value in the radix specified by the second
   * argument.
   *
   * <p>If the radix is smaller than {@code Character.MIN_RADIX}
   * or larger than {@code Character.MAX_RADIX}, then the radix
   * {@code 10} is used instead.
   *
   * <p>Note that since the first argument is treated as an unsigned
   * value, no leading sign character is printed.
   *
   * <p>If the magnitude is zero, it is represented by a single zero
   * character {@code '0'} ({@code '\u005Cu0030'}); otherwise,
   * the first character of the representation of the magnitude will
   * not be the zero character.
   *
   * <p>The behavior of radixes and the characters used as digits
   * are the same as {@link #toString(int, int) toString}.
   *
   * @param i an integer to be converted to an unsigned string.
   * @param radix the radix to use in the string representation.
   * @return an unsigned string representation of the argument in the specified radix.
   * @see #toString(int, int)
   * @since 1.8
   */
  public static String toUnsignedString(int i, int radix) {
    return Long.toUnsignedString(toUnsignedLong(i), radix);
  }

  /**
   * Returns a string representation of the integer argument as an
   * unsigned integer in base&nbsp;16.
   *
   * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
   * if the argument is negative; otherwise, it is equal to the
   * argument.  This value is converted to a string of ASCII digits
   * in hexadecimal (base&nbsp;16) with no extra leading
   * {@code 0}s.
   *
   * <p>The value of the argument can be recovered from the returned
   * string {@code s} by calling {@link
   * Integer#parseUnsignedInt(String, int)
   * Integer.parseUnsignedInt(s, 16)}.
   *
   * <p>If the unsigned magnitude is zero, it is represented by a
   * single zero character {@code '0'} ({@code '\u005Cu0030'});
   * otherwise, the first character of the representation of the
   * unsigned magnitude will not be the zero character. The
   * following characters are used as hexadecimal digits:
   *
   * <blockquote>
   * {@code 0123456789abcdef}
   * </blockquote>
   *
   * These are the characters {@code '\u005Cu0030'} through
   * {@code '\u005Cu0039'} and {@code '\u005Cu0061'} through
   * {@code '\u005Cu0066'}. If uppercase letters are
   * desired, the {@link java.lang.String#toUpperCase()} method may
   * be called on the result:
   *
   * <blockquote>
   * {@code Integer.toHexString(n).toUpperCase()}
   * </blockquote>
   *
   * @param i an integer to be converted to a string.
   * @return the string representation of the unsigned integer value represented by the argument in
   * hexadecimal (base&nbsp;16).
   * @see #parseUnsignedInt(String, int)
   * @see #toUnsignedString(int, int)
   * @since JDK1.0.2
   */
  public static String toHexString(int i) {
    return toUnsignedString0(i, 4);
  }

  /**
   * Returns a string representation of the integer argument as an
   * unsigned integer in base&nbsp;8.
   *
   * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
   * if the argument is negative; otherwise, it is equal to the
   * argument.  This value is converted to a string of ASCII digits
   * in octal (base&nbsp;8) with no extra leading {@code 0}s.
   *
   * <p>The value of the argument can be recovered from the returned
   * string {@code s} by calling {@link
   * Integer#parseUnsignedInt(String, int)
   * Integer.parseUnsignedInt(s, 8)}.
   *
   * <p>If the unsigned magnitude is zero, it is represented by a
   * single zero character {@code '0'} ({@code '\u005Cu0030'});
   * otherwise, the first character of the representation of the
   * unsigned magnitude will not be the zero character. The
   * following characters are used as octal digits:
   *
   * <blockquote>
   * {@code 01234567}
   * </blockquote>
   *
   * These are the characters {@code '\u005Cu0030'} through
   * {@code '\u005Cu0037'}.
   *
   * @param i an integer to be converted to a string.
   * @return the string representation of the unsigned integer value represented by the argument in
   * octal (base&nbsp;8).
   * @see #parseUnsignedInt(String, int)
   * @see #toUnsignedString(int, int)
   * @since JDK1.0.2
   */
  public static String toOctalString(int i) {
    return toUnsignedString0(i, 3);
  }

  /**
   * Returns a string representation of the integer argument as an
   * unsigned integer in base&nbsp;2.
   *
   * <p>The unsigned integer value is the argument plus 2<sup>32</sup>
   * if the argument is negative; otherwise it is equal to the
   * argument.  This value is converted to a string of ASCII digits
   * in binary (base&nbsp;2) with no extra leading {@code 0}s.
   *
   * <p>The value of the argument can be recovered from the returned
   * string {@code s} by calling {@link
   * Integer#parseUnsignedInt(String, int)
   * Integer.parseUnsignedInt(s, 2)}.
   *
   * <p>If the unsigned magnitude is zero, it is represented by a
   * single zero character {@code '0'} ({@code '\u005Cu0030'});
   * otherwise, the first character of the representation of the
   * unsigned magnitude will not be the zero character. The
   * characters {@code '0'} ({@code '\u005Cu0030'}) and {@code
   * '1'} ({@code '\u005Cu0031'}) are used as binary digits.
   *
   * @param i an integer to be converted to a string.
   * @return the string representation of the unsigned integer value represented by the argument in
   * binary (base&nbsp;2).
   * @see #parseUnsignedInt(String, int)
   * @see #toUnsignedString(int, int)
   * @since JDK1.0.2
   */
  public static String toBinaryString(int i) {
    return toUnsignedString0(i, 1);
  }

  /**
   * Convert the integer to an unsigned number.
   */
  private static String toUnsignedString0(int val, int shift) {
    // assert shift > 0 && shift <=5 : "Illegal shift value";
    int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
    int chars = Math.max(((mag + (shift - 1)) / shift), 1);
    char[] buf = new char[chars];

    formatUnsignedInt(val, shift, buf, 0, chars);

    // Use special constructor which takes over "buf".
    return new String(buf, true);
  }

  /**
   * Format a long (treated as unsigned) into a character buffer.
   *
   * @param val the unsigned int to format
   * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
   * @param buf the character buffer to write to
   * @param offset the offset in the destination buffer to start at
   * @param len the number of characters to write
   * @return the lowest character  location used
   */
  static int formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
    int charPos = len;
    int radix = 1 << shift;
    int mask = radix - 1;
    do {
      buf[offset + --charPos] = Integer.digits[val & mask];
      val >>>= shift;
    } while (val != 0 && charPos > 0);

    return charPos;
  }

  final static char[] DigitTens = {
      '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
      '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
      '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
      '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
      '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
      '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
      '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
      '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
      '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
      '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
  };

  final static char[] DigitOnes = {
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
      '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
  };

  // I use the "invariant division by multiplication" trick to
  // accelerate Integer.toString.  In particular we want to
  // avoid division by 10.
  //
  // The "trick" has roughly the same performance characteristics
  // as the "classic" Integer.toString code on a non-JIT VM.
  // The trick avoids .rem and .div calls but has a longer code
  // path and is thus dominated by dispatch overhead.  In the
  // JIT case the dispatch overhead doesn't exist and the
  // "trick" is considerably faster than the classic code.
  //
  // TODO-FIXME: convert (x * 52429) into the equiv shift-add
  // sequence.
  //
  // RE:  Division by Invariant Integers using Multiplication
  //      T Gralund, P Montgomery
  //      ACM PLDI 1994
  //

  /**
   * Returns a {@code String} object representing the
   * specified integer. The argument is converted to signed decimal
   * representation and returned as a string, exactly as if the
   * argument and radix 10 were given as arguments to the {@link
   * #toString(int, int)} method.
   *
   * @param i an integer to be converted.
   * @return a string representation of the argument in base&nbsp;10.
   */
  public static String toString(int i) {
    if (i == Integer.MIN_VALUE) {
      return "-2147483648";
    }
    int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
    char[] buf = new char[size];
    getChars(i, size, buf);
    return new String(buf, true);
  }

  /**
   * Returns a string representation of the argument as an unsigned
   * decimal value.
   *
   * The argument is converted to unsigned decimal representation
   * and returned as a string exactly as if the argument and radix
   * 10 were given as arguments to the {@link #toUnsignedString(int,
   * int)} method.
   *
   * @param i an integer to be converted to an unsigned string.
   * @return an unsigned string representation of the argument.
   * @see #toUnsignedString(int, int)
   * @since 1.8
   */
  public static String toUnsignedString(int i) {
    return Long.toString(toUnsignedLong(i));
  }

  /**
   * Places characters representing the integer i into the
   * character array buf. The characters are placed into
   * the buffer backwards starting with the least significant
   * digit at the specified index (exclusive), and working
   * backwards from there.
   *
   * Will fail if i == Integer.MIN_VALUE
   */
  static void getChars(int i, int index, char[] buf) {
    int q, r;
    int charPos = index;
    char sign = 0;

    if (i < 0) {
      sign = '-';
      i = -i;
    }

    // Generate two digits per iteration
    while (i >= 65536) {
      q = i / 100;
      // really: r = i - (q * 100);
      r = i - ((q << 6) + (q << 5) + (q << 2));
      i = q;
      buf[--charPos] = DigitOnes[r];
      buf[--charPos] = DigitTens[r];
    }

    // Fall thru to fast mode for smaller numbers
    // assert(i <= 65536, i);
    for (; ; ) {
      q = (i * 52429) >>> (16 + 3);
      r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ...
      buf[--charPos] = digits[r];
      i = q;
      if (i == 0) {
        break;
      }
    }
    if (sign != 0) {
      buf[--charPos] = sign;
    }
  }

  final static int[] sizeTable = {9, 99, 999, 9999, 99999, 999999, 9999999,
      99999999, 999999999, Integer.MAX_VALUE};

  // Requires positive x
  static int stringSize(int x) {
    for (int i = 0; ; i++) {
      if (x <= sizeTable[i]) {
        return i + 1;
      }
    }
  }

  /**
   * Parses the string argument as a signed integer in the radix
   * specified by the second argument. The characters in the string
   * must all be digits of the specified radix (as determined by
   * whether {@link java.lang.Character#digit(char, int)} returns a
   * nonnegative value), except that the first character may be an
   * ASCII minus sign {@code '-'} ({@code '\u005Cu002D'}) to
   * indicate a negative value or an ASCII plus sign {@code '+'}
   * ({@code '\u005Cu002B'}) to indicate a positive value. The
   * resulting integer value is returned.
   *
   * <p>An exception of type {@code NumberFormatException} is
   * thrown if any of the following situations occurs:
   * <ul>
   * <li>The first argument is {@code null} or is a string of
   * length zero.
   *
   * <li>The radix is either smaller than
   * {@link java.lang.Character#MIN_RADIX} or
   * larger than {@link java.lang.Character#MAX_RADIX}.
   *
   * <li>Any character of the string is not a digit of the specified
   * radix, except that the first character may be a minus sign
   * {@code '-'} ({@code '\u005Cu002D'}) or plus sign
   * {@code '+'} ({@code '\u005Cu002B'}) provided that the
   * string is longer than length 1.
   *
   * <li>The value represented by the string is not a value of type
   * {@code int}.
   * </ul>
   *
   * <p>Examples:
   * <blockquote><pre>
   * parseInt("0", 10) returns 0
   * parseInt("473", 10) returns 473
   * parseInt("+42", 10) returns 42
   * parseInt("-0", 10) returns 0
   * parseInt("-FF", 16) returns -255
   * parseInt("1100110", 2) returns 102
   * parseInt("2147483647", 10) returns 2147483647
   * parseInt("-2147483648", 10) returns -2147483648
   * parseInt("2147483648", 10) throws a NumberFormatException
   * parseInt("99", 8) throws a NumberFormatException
   * parseInt("Kona", 10) throws a NumberFormatException
   * parseInt("Kona", 27) returns 411787
   * </pre></blockquote>
   *
   * @param s the {@code String} containing the integer representation to be parsed
   * @param radix the radix to be used while parsing {@code s}.
   * @return the integer represented by the string argument in the specified radix.
   * @throws NumberFormatException if the {@code String} does not contain a parsable {@code int}.
   */
  public static int parseInt(String s, int radix)
      throws NumberFormatException {
        /*
         * WARNING: This method may be invoked early during VM initialization
         * before IntegerCache is initialized. Care must be taken to not use
         * the valueOf method.
         */

    if (s == null) {
      throw new NumberFormatException("null");
    }

    if (radix < Character.MIN_RADIX) {
      throw new NumberFormatException("radix " + radix +
          " less than Character.MIN_RADIX");
    }

    if (radix > Character.MAX_RADIX) {
      throw new NumberFormatException("radix " + radix +
          " greater than Character.MAX_RADIX");
    }

    int result = 0;
    boolean negative = false;
    int i = 0, len = s.length();
    int limit = -Integer.MAX_VALUE;
    int multmin;
    int digit;

    if (len > 0) {
      char firstChar = s.charAt(0);
      if (firstChar < '0') { // Possible leading "+" or "-"
        if (firstChar == '-') {
          negative = true;
          limit = Integer.MIN_VALUE;
        } else if (firstChar != '+') {
          throw NumberFormatException.forInputString(s);
        }

        if (len == 1) // Cannot have lone "+" or "-"
        {
          throw NumberFormatException.forInputString(s);
        }
        i++;
      }
      multmin = limit / radix;
      while (i < len) {
        // Accumulating negatively avoids surprises near MAX_VALUE
        digit = Character.digit(s.charAt(i++), radix);
        if (digit < 0) {
          throw NumberFormatException.forInputString(s);
        }
        if (result < multmin) {
          throw NumberFormatException.forInputString(s);
        }
        result *= radix;
        if (result < limit + digit) {
          throw NumberFormatException.forInputString(s);
        }
        result -= digit;
      }
    } else {
      throw NumberFormatException.forInputString(s);
    }
    return negative ? result : -result;
  }

  /**
   * Parses the string argument as a signed decimal integer. The
   * characters in the string must all be decimal digits, except
   * that the first character may be an ASCII minus sign {@code '-'}
   * ({@code '\u005Cu002D'}) to indicate a negative value or an
   * ASCII plus sign {@code '+'} ({@code '\u005Cu002B'}) to
   * indicate a positive value. The resulting integer value is
   * returned, exactly as if the argument and the radix 10 were
   * given as arguments to the {@link #parseInt(java.lang.String,
   * int)} method.
   *
   * @param s a {@code String} containing the {@code int} representation to be parsed
   * @return the integer value represented by the argument in decimal.
   * @throws NumberFormatException if the string does not contain a parsable integer.
   */
  public static int parseInt(String s) throws NumberFormatException {
    return parseInt(s, 10);
  }

  /**
   * Parses the string argument as an unsigned integer in the radix
   * specified by the second argument.  An unsigned integer maps the
   * values usually associated with negative numbers to positive
   * numbers larger than {@code MAX_VALUE}.
   *
   * The characters in the string must all be digits of the
   * specified radix (as determined by whether {@link
   * java.lang.Character#digit(char, int)} returns a nonnegative
   * value), except that the first character may be an ASCII plus
   * sign {@code '+'} ({@code '\u005Cu002B'}). The resulting
   * integer value is returned.
   *
   * <p>An exception of type {@code NumberFormatException} is
   * thrown if any of the following situations occurs:
   * <ul>
   * <li>The first argument is {@code null} or is a string of
   * length zero.
   *
   * <li>The radix is either smaller than
   * {@link java.lang.Character#MIN_RADIX} or
   * larger than {@link java.lang.Character#MAX_RADIX}.
   *
   * <li>Any character of the string is not a digit of the specified
   * radix, except that the first character may be a plus sign
   * {@code '+'} ({@code '\u005Cu002B'}) provided that the
   * string is longer than length 1.
   *
   * <li>The value represented by the string is larger than the
   * largest unsigned {@code int}, 2<sup>32</sup>-1.
   *
   * </ul>
   *
   * @param s the {@code String} containing the unsigned integer representation to be parsed
   * @param radix the radix to be used while parsing {@code s}.
   * @return the integer represented by the string argument in the specified radix.
   * @throws NumberFormatException if the {@code String} does not contain a parsable {@code int}.
   * @since 1.8
   */
  public static int parseUnsignedInt(String s, int radix)
      throws NumberFormatException {
    if (s == null) {
      throw new NumberFormatException("null");
    }

    int len = s.length();
    if (len > 0) {
      char firstChar = s.charAt(0);
      if (firstChar == '-') {
        throw new
            NumberFormatException(String.format("Illegal leading minus sign " +
            "on unsigned string %s.", s));
      } else {
        if (len <= 5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
            (radix == 10 && len <= 9)) { // Integer.MAX_VALUE in base 10 is 10 digits
          return parseInt(s, radix);
        } else {
          long ell = Long.parseLong(s, radix);
          if ((ell & 0xffff_ffff_0000_0000L) == 0) {
            return (int) ell;
          } else {
            throw new
                NumberFormatException(String.format("String value %s exceeds " +
                "range of unsigned int.", s));
          }
        }
      }
    } else {
      throw NumberFormatException.forInputString(s);
    }
  }

  /**
   * Parses the string argument as an unsigned decimal integer. The
   * characters in the string must all be decimal digits, except
   * that the first character may be an an ASCII plus sign {@code
   * '+'} ({@code '\u005Cu002B'}). The resulting integer value
   * is returned, exactly as if the argument and the radix 10 were
   * given as arguments to the {@link
   * #parseUnsignedInt(java.lang.String, int)} method.
   *
   * @param s a {@code String} containing the unsigned {@code int} representation to be parsed
   * @return the unsigned integer value represented by the argument in decimal.
   * @throws NumberFormatException if the string does not contain a parsable unsigned integer.
   * @since 1.8
   */
  public static int parseUnsignedInt(String s) throws NumberFormatException {
    return parseUnsignedInt(s, 10);
  }

  /**
   * Returns an {@code Integer} object holding the value
   * extracted from the specified {@code String} when parsed
   * with the radix given by the second argument. The first argument
   * is interpreted as representing a signed integer in the radix
   * specified by the second argument, exactly as if the arguments
   * were given to the {@link #parseInt(java.lang.String, int)}
   * method. The result is an {@code Integer} object that
   * represents the integer value specified by the string.
   *
   * <p>In other words, this method returns an {@code Integer}
   * object equal to the value of:
   *
   * <blockquote>
   * {@code new Integer(Integer.parseInt(s, radix))}
   * </blockquote>
   *
   * @param s the string to be parsed.
   * @param radix the radix to be used in interpreting {@code s}
   * @return an {@code Integer} object holding the value represented by the string argument in the
   * specified radix.
   * @throws NumberFormatException if the {@code String} does not contain a parsable {@code int}.
   */
  public static Integer valueOf(String s, int radix) throws NumberFormatException {
    return Integer.valueOf(parseInt(s, radix));
  }

  /**
   * Returns an {@code Integer} object holding the
   * value of the specified {@code String}. The argument is
   * interpreted as representing a signed decimal integer, exactly
   * as if the argument were given to the {@link
   * #parseInt(java.lang.String)} method. The result is an
   * {@code Integer} object that represents the integer value
   * specified by the string.
   *
   * <p>In other words, this method returns an {@code Integer}
   * object equal to the value of:
   *
   * <blockquote>
   * {@code new Integer(Integer.parseInt(s))}
   * </blockquote>
   *
   * @param s the string to be parsed.
   * @return an {@code Integer} object holding the value represented by the string argument.
   * @throws NumberFormatException if the string cannot be parsed as an integer.
   */
  public static Integer valueOf(String s) throws NumberFormatException {
    return Integer.valueOf(parseInt(s, 10));
  }

  /**
   * Cache to support the object identity semantics of autoboxing for values between
   * -128 and 127 (inclusive) as required by JLS.
   *
   * The cache is initialized on first usage.  The size of the cache
   * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
   * During VM initialization, java.lang.Integer.IntegerCache.high property
   * may be set and saved in the private system properties in the
   * sun.misc.VM class.
   */

  private static class IntegerCache {

    static final int low = -128;
    static final int high;
    static final Integer cache[];

    static {
      // high value may be configured by property
      int h = 127;
      String integerCacheHighPropValue =
          sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
      if (integerCacheHighPropValue != null) {
        try {
          int i = parseInt(integerCacheHighPropValue);
          i = Math.max(i, 127);
          // Maximum array size is Integer.MAX_VALUE
          h = Math.min(i, Integer.MAX_VALUE - (-low) - 1);
        } catch (NumberFormatException nfe) {
          // If the property cannot be parsed into an int, ignore it.
        }
      }
      high = h;

      cache = new Integer[(high - low) + 1];
      int j = low;
      for (int k = 0; k < cache.length; k++) {
        cache[k] = new Integer(j++);
      }

      // range [-128, 127] must be interned (JLS7 5.1.7)
      assert IntegerCache.high >= 127;
    }

    private IntegerCache() {
    }
  }

  /**
   * Returns an {@code Integer} instance representing the specified
   * {@code int} value.  If a new {@code Integer} instance is not
   * required, this method should generally be used in preference to
   * the constructor {@link #Integer(int)}, as this method is likely
   * to yield significantly better space and time performance by
   * caching frequently requested values.
   *
   * This method will always cache values in the range -128 to 127,
   * inclusive, and may cache other values outside of this range.
   *
   * @param i an {@code int} value.
   * @return an {@code Integer} instance representing {@code i}.
   * @since 1.5
   */
  public static Integer valueOf(int i) {
    if (i >= IntegerCache.low && i <= IntegerCache.high) {
      return IntegerCache.cache[i + (-IntegerCache.low)];
    }
    return new Integer(i);
  }

  /**
   * The value of the {@code Integer}.
   *
   * @serial
   */
  private final int value;

  /**
   * Constructs a newly allocated {@code Integer} object that
   * represents the specified {@code int} value.
   *
   * @param value the value to be represented by the {@code Integer} object.
   */
  public Integer(int value) {
    this.value = value;
  }

  /**
   * Constructs a newly allocated {@code Integer} object that
   * represents the {@code int} value indicated by the
   * {@code String} parameter. The string is converted to an
   * {@code int} value in exactly the manner used by the
   * {@code parseInt} method for radix 10.
   *
   * @param s the {@code String} to be converted to an {@code Integer}.
   * @throws NumberFormatException if the {@code String} does not contain a parsable integer.
   * @see java.lang.Integer#parseInt(java.lang.String, int)
   */
  public Integer(String s) throws NumberFormatException {
    this.value = parseInt(s, 10);
  }

  /**
   * Returns the value of this {@code Integer} as a {@code byte}
   * after a narrowing primitive conversion.
   *
   * @jls 5.1.3 Narrowing Primitive Conversions
   */
  public byte byteValue() {
    return (byte) value;
  }

  /**
   * Returns the value of this {@code Integer} as a {@code short}
   * after a narrowing primitive conversion.
   *
   * @jls 5.1.3 Narrowing Primitive Conversions
   */
  public short shortValue() {
    return (short) value;
  }

  /**
   * Returns the value of this {@code Integer} as an
   * {@code int}.
   */
  public int intValue() {
    return value;
  }

  /**
   * Returns the value of this {@code Integer} as a {@code long}
   * after a widening primitive conversion.
   *
   * @jls 5.1.2 Widening Primitive Conversions
   * @see Integer#toUnsignedLong(int)
   */
  public long longValue() {
    return (long) value;
  }

  /**
   * Returns the value of this {@code Integer} as a {@code float}
   * after a widening primitive conversion.
   *
   * @jls 5.1.2 Widening Primitive Conversions
   */
  public float floatValue() {
    return (float) value;
  }

  /**
   * Returns the value of this {@code Integer} as a {@code double}
   * after a widening primitive conversion.
   *
   * @jls 5.1.2 Widening Primitive Conversions
   */
  public double doubleValue() {
    return (double) value;
  }

  /**
   * Returns a {@code String} object representing this
   * {@code Integer}'s value. The value is converted to signed
   * decimal representation and returned as a string, exactly as if
   * the integer value were given as an argument to the {@link
   * java.lang.Integer#toString(int)} method.
   *
   * @return a string representation of the value of this object in base&nbsp;10.
   */
  public String toString() {
    return toString(value);
  }

  /**
   * Returns a hash code for this {@code Integer}.
   *
   * @return a hash code value for this object, equal to the primitive {@code int} value represented
   * by this {@code Integer} object.
   */
  @Override
  public int hashCode() {
    return Integer.hashCode(value);
  }

  /**
   * Returns a hash code for a {@code int} value; compatible with
   * {@code Integer.hashCode()}.
   *
   * @param value the value to hash
   * @return a hash code value for a {@code int} value.
   * @since 1.8
   */
  public static int hashCode(int value) {
    return value;
  }

  /**
   * Compares this object to the specified object.  The result is
   * {@code true} if and only if the argument is not
   * {@code null} and is an {@code Integer} object that
   * contains the same {@code int} value as this object.
   *
   * @param obj the object to compare with.
   * @return {@code true} if the objects are the same; {@code false} otherwise.
   */
  public boolean equals(Object obj) {
    if (obj instanceof Integer) {
      return value == ((Integer) obj).intValue();
    }
    return false;
  }

  /**
   * Determines the integer value of the system property with the
   * specified name.
   *
   * <p>The first argument is treated as the name of a system
   * property.  System properties are accessible through the {@link
   * java.lang.System#getProperty(java.lang.String)} method. The
   * string value of this property is then interpreted as an integer
   * value using the grammar supported by {@link Integer#decode decode} and
   * an {@code Integer} object representing this value is returned.
   *
   * <p>If there is no property with the specified name, if the
   * specified name is empty or {@code null}, or if the property
   * does not have the correct numeric format, then {@code null} is
   * returned.
   *
   * <p>In other words, this method returns an {@code Integer}
   * object equal to the value of:
   *
   * <blockquote>
   * {@code getInteger(nm, null)}
   * </blockquote>
   *
   * @param nm property name.
   * @return the {@code Integer} value of the property.
   * @throws SecurityException for the same reasons as {@link System#getProperty(String)
   * System.getProperty}
   * @see java.lang.System#getProperty(java.lang.String)
   * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
   */
  public static Integer getInteger(String nm) {
    return getInteger(nm, null);
  }

  /**
   * Determines the integer value of the system property with the
   * specified name.
   *
   * <p>The first argument is treated as the name of a system
   * property.  System properties are accessible through the {@link
   * java.lang.System#getProperty(java.lang.String)} method. The
   * string value of this property is then interpreted as an integer
   * value using the grammar supported by {@link Integer#decode decode} and
   * an {@code Integer} object representing this value is returned.
   *
   * <p>The second argument is the default value. An {@code Integer} object
   * that represents the value of the second argument is returned if there
   * is no property of the specified name, if the property does not have
   * the correct numeric format, or if the specified name is empty or
   * {@code null}.
   *
   * <p>In other words, this method returns an {@code Integer} object
   * equal to the value of:
   *
   * <blockquote>
   * {@code getInteger(nm, new Integer(val))}
   * </blockquote>
   *
   * but in practice it may be implemented in a manner such as:
   *
   * <blockquote><pre>
   * Integer result = getInteger(nm, null);
   * return (result == null) ? new Integer(val) : result;
   * </pre></blockquote>
   *
   * to avoid the unnecessary allocation of an {@code Integer}
   * object when the default value is not needed.
   *
   * @param nm property name.
   * @param val default value.
   * @return the {@code Integer} value of the property.
   * @throws SecurityException for the same reasons as {@link System#getProperty(String)
   * System.getProperty}
   * @see java.lang.System#getProperty(java.lang.String)
   * @see java.lang.System#getProperty(java.lang.String, java.lang.String)
   */
  public static Integer getInteger(String nm, int val) {
    Integer result = getInteger(nm, null);
    return (result == null) ? Integer.valueOf(val) : result;
  }

  /**
   * Returns the integer value of the system property with the
   * specified name.  The first argument is treated as the name of a
   * system property.  System properties are accessible through the
   * {@link java.lang.System#getProperty(java.lang.String)} method.
   * The string value of this property is then interpreted as an
   * integer value, as per the {@link Integer#decode decode} method,
   * and an {@code Integer} object representing this value is
   * returned; in summary:
   *
   * <ul><li>If the property value begins with the two ASCII characters
   * {@code 0x} or the ASCII character {@code #}, not
   * followed by a minus sign, then the rest of it is parsed as a
   * hexadecimal integer exactly as by the method
   * {@link #valueOf(java.lang.String, int)} with radix 16.
   * <li>If the property value begins with the ASCII character
   * {@code 0} followed by another character, it is parsed as an
   * octal integer exactly as by the method
   * {@link #valueOf(java.lang.String, int)} with radix 8.
   * <li>Otherwise, the property value is parsed as a decimal integer
   * exactly as by the method {@link #valueOf(java.lang.String, int)}
   * with radix 10.
   * </ul>
   *
   * <p>The second argument is the default value. The default value is
   * returned if there is no property of the specified name, if the
   * property does not have the correct numeric format, or if the
   * specified name is empty or {@code null}.
   *
   * @param nm property name.
   * @param val default value.
   * @return the {@code Integer} value of the property.
   * @throws SecurityException for the same reasons as {@link System#getProperty(String)
   * System.getProperty}
   * @see System#getProperty(java.lang.String)
   * @see System#getProperty(java.lang.String, java.lang.String)
   */
  public static Integer getInteger(String nm, Integer val) {
    String v = null;
    try {
      v = System.getProperty(nm);
    } catch (IllegalArgumentException | NullPointerException e) {
    }
    if (v != null) {
      try {
        return Integer.decode(v);
      } catch (NumberFormatException e) {
      }
    }
    return val;
  }

  /**
   * Decodes a {@code String} into an {@code Integer}.
   * Accepts decimal, hexadecimal, and octal numbers given
   * by the following grammar:
   *
   * <blockquote>
   * <dl>
   * <dt><i>DecodableString:</i>
   * <dd><i>Sign<sub>opt</sub> DecimalNumeral</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code 0x} <i>HexDigits</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code 0X} <i>HexDigits</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code #} <i>HexDigits</i>
   * <dd><i>Sign<sub>opt</sub></i> {@code 0} <i>OctalDigits</i>
   *
   * <dt><i>Sign:</i>
   * <dd>{@code -}
   * <dd>{@code +}
   * </dl>
   * </blockquote>
   *
   * <i>DecimalNumeral</i>, <i>HexDigits</i>, and <i>OctalDigits</i>
   * are as defined in section 3.10.1 of
   * <cite>The Java&trade; Language Specification</cite>,
   * except that underscores are not accepted between digits.
   *
   * <p>The sequence of characters following an optional
   * sign and/or radix specifier ("{@code 0x}", "{@code 0X}",
   * "{@code #}", or leading zero) is parsed as by the {@code
   * Integer.parseInt} method with the indicated radix (10, 16, or
   * 8).  This sequence of characters must represent a positive
   * value or a {@link NumberFormatException} will be thrown.  The
   * result is negated if first character of the specified {@code
   * String} is the minus sign.  No whitespace characters are
   * permitted in the {@code String}.
   *
   * @param nm the {@code String} to decode.
   * @return an {@code Integer} object holding the {@code int} value represented by {@code nm}
   * @throws NumberFormatException if the {@code String} does not contain a parsable integer.
   * @see java.lang.Integer#parseInt(java.lang.String, int)
   */
  public static Integer decode(String nm) throws NumberFormatException {
    int radix = 10;
    int index = 0;
    boolean negative = false;
    Integer result;

    if (nm.length() == 0) {
      throw new NumberFormatException("Zero length string");
    }
    char firstChar = nm.charAt(0);
    // Handle sign, if present
    if (firstChar == '-') {
      negative = true;
      index++;
    } else if (firstChar == '+') {
      index++;
    }

    // Handle radix specifier, if present
    if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
      index += 2;
      radix = 16;
    } else if (nm.startsWith("#", index)) {
      index++;
      radix = 16;
    } else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
      index++;
      radix = 8;
    }

    if (nm.startsWith("-", index) || nm.startsWith("+", index)) {
      throw new NumberFormatException("Sign character in wrong position");
    }

    try {
      result = Integer.valueOf(nm.substring(index), radix);
      result = negative ? Integer.valueOf(-result.intValue()) : result;
    } catch (NumberFormatException e) {
      // If number is Integer.MIN_VALUE, we'll end up here. The next line
      // handles this case, and causes any genuine format error to be
      // rethrown.
      String constant = negative ? ("-" + nm.substring(index))
          : nm.substring(index);
      result = Integer.valueOf(constant, radix);
    }
    return result;
  }

  /**
   * Compares two {@code Integer} objects numerically.
   *
   * @param anotherInteger the {@code Integer} to be compared.
   * @return the value {@code 0} if this {@code Integer} is equal to the argument {@code Integer}; a
   * value less than {@code 0} if this {@code Integer} is numerically less than the argument {@code
   * Integer}; and a value greater than {@code 0} if this {@code Integer} is numerically greater
   * than the argument {@code Integer} (signed comparison).
   * @since 1.2
   */
  public int compareTo(Integer anotherInteger) {
    return compare(this.value, anotherInteger.value);
  }

  /**
   * Compares two {@code int} values numerically.
   * The value returned is identical to what would be returned by:
   * <pre>
   *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
   * </pre>
   *
   * @param x the first {@code int} to compare
   * @param y the second {@code int} to compare
   * @return the value {@code 0} if {@code x == y}; a value less than {@code 0} if {@code x < y};
   * and a value greater than {@code 0} if {@code x > y}
   * @since 1.7
   */
  public static int compare(int x, int y) {
    return (x < y) ? -1 : ((x == y) ? 0 : 1);
  }

  /**
   * Compares two {@code int} values numerically treating the values
   * as unsigned.
   *
   * @param x the first {@code int} to compare
   * @param y the second {@code int} to compare
   * @return the value {@code 0} if {@code x == y}; a value less than {@code 0} if {@code x < y} as
   * unsigned values; and a value greater than {@code 0} if {@code x > y} as unsigned values
   * @since 1.8
   */
  public static int compareUnsigned(int x, int y) {
    return compare(x + MIN_VALUE, y + MIN_VALUE);
  }

  /**
   * Converts the argument to a {@code long} by an unsigned
   * conversion.  In an unsigned conversion to a {@code long}, the
   * high-order 32 bits of the {@code long} are zero and the
   * low-order 32 bits are equal to the bits of the integer
   * argument.
   *
   * Consequently, zero and positive {@code int} values are mapped
   * to a numerically equal {@code long} value and negative {@code
   * int} values are mapped to a {@code long} value equal to the
   * input plus 2<sup>32</sup>.
   *
   * @param x the value to convert to an unsigned {@code long}
   * @return the argument converted to {@code long} by an unsigned conversion
   * @since 1.8
   */
  public static long toUnsignedLong(int x) {
    return ((long) x) & 0xffffffffL;
  }

  /**
   * Returns the unsigned quotient of dividing the first argument by
   * the second where each argument and the result is interpreted as
   * an unsigned value.
   *
   * <p>Note that in two's complement arithmetic, the three other
   * basic arithmetic operations of add, subtract, and multiply are
   * bit-wise identical if the two operands are regarded as both
   * being signed or both being unsigned.  Therefore separate {@code
   * addUnsigned}, etc. methods are not provided.
   *
   * @param dividend the value to be divided
   * @param divisor the value doing the dividing
   * @return the unsigned quotient of the first argument divided by the second argument
   * @see #remainderUnsigned
   * @since 1.8
   */
  public static int divideUnsigned(int dividend, int divisor) {
    // In lieu of tricky code, for now just use long arithmetic.
    return (int) (toUnsignedLong(dividend) / toUnsignedLong(divisor));
  }

  /**
   * Returns the unsigned remainder from dividing the first argument
   * by the second where each argument and the result is interpreted
   * as an unsigned value.
   *
   * @param dividend the value to be divided
   * @param divisor the value doing the dividing
   * @return the unsigned remainder of the first argument divided by the second argument
   * @see #divideUnsigned
   * @since 1.8
   */
  public static int remainderUnsigned(int dividend, int divisor) {
    // In lieu of tricky code, for now just use long arithmetic.
    return (int) (toUnsignedLong(dividend) % toUnsignedLong(divisor));
  }

  // Bit twiddling

  /**
   * The number of bits used to represent an {@code int} value in two's
   * complement binary form.
   *
   * @since 1.5
   */
  @Native
  public static final int SIZE = 32;

  /**
   * The number of bytes used to represent a {@code int} value in two's
   * complement binary form.
   *
   * @since 1.8
   */
  public static final int BYTES = SIZE / Byte.SIZE;

  /**
   * Returns an {@code int} value with at most a single one-bit, in the
   * position of the highest-order ("leftmost") one-bit in the specified
   * {@code int} value.  Returns zero if the specified value has no
   * one-bits in its two's complement binary representation, that is, if it
   * is equal to zero.
   *
   * @param i the value whose highest one bit is to be computed
   * @return an {@code int} value with a single one-bit, in the position of the highest-order
   * one-bit in the specified value, or zero if the specified value is itself equal to zero.
   * @since 1.5
   */
  public static int highestOneBit(int i) {
    // HD, Figure 3-1
    i |= (i >> 1);
    i |= (i >> 2);
    i |= (i >> 4);
    i |= (i >> 8);
    i |= (i >> 16);
    return i - (i >>> 1);
  }

  /**
   * Returns an {@code int} value with at most a single one-bit, in the
   * position of the lowest-order ("rightmost") one-bit in the specified
   * {@code int} value.  Returns zero if the specified value has no
   * one-bits in its two's complement binary representation, that is, if it
   * is equal to zero.
   *
   * @param i the value whose lowest one bit is to be computed
   * @return an {@code int} value with a single one-bit, in the position of the lowest-order one-bit
   * in the specified value, or zero if the specified value is itself equal to zero.
   * @since 1.5
   */
  public static int lowestOneBit(int i) {
    // HD, Section 2-1
    return i & -i;
  }

  /**
   * Returns the number of zero bits preceding the highest-order
   * ("leftmost") one-bit in the two's complement binary representation
   * of the specified {@code int} value.  Returns 32 if the
   * specified value has no one-bits in its two's complement representation,
   * in other words if it is equal to zero.
   *
   * <p>Note that this method is closely related to the logarithm base 2.
   * For all positive {@code int} values x:
   * <ul>
   * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
   * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
   * </ul>
   *
   * @param i the value whose number of leading zeros is to be computed
   * @return the number of zero bits preceding the highest-order ("leftmost") one-bit in the two's
   * complement binary representation of the specified {@code int} value, or 32 if the value is
   * equal to zero.
   * @since 1.5
   */
  public static int numberOfLeadingZeros(int i) {
    // HD, Figure 5-6
    if (i == 0) {
      return 32;
    }
    int n = 1;
    if (i >>> 16 == 0) {
      n += 16;
      i <<= 16;
    }
    if (i >>> 24 == 0) {
      n += 8;
      i <<= 8;
    }
    if (i >>> 28 == 0) {
      n += 4;
      i <<= 4;
    }
    if (i >>> 30 == 0) {
      n += 2;
      i <<= 2;
    }
    n -= i >>> 31;
    return n;
  }

  /**
   * Returns the number of zero bits following the lowest-order ("rightmost")
   * one-bit in the two's complement binary representation of the specified
   * {@code int} value.  Returns 32 if the specified value has no
   * one-bits in its two's complement representation, in other words if it is
   * equal to zero.
   *
   * @param i the value whose number of trailing zeros is to be computed
   * @return the number of zero bits following the lowest-order ("rightmost") one-bit in the two's
   * complement binary representation of the specified {@code int} value, or 32 if the value is
   * equal to zero.
   * @since 1.5
   */
  public static int numberOfTrailingZeros(int i) {
    // HD, Figure 5-14
    int y;
    if (i == 0) {
      return 32;
    }
    int n = 31;
    y = i << 16;
    if (y != 0) {
      n = n - 16;
      i = y;
    }
    y = i << 8;
    if (y != 0) {
      n = n - 8;
      i = y;
    }
    y = i << 4;
    if (y != 0) {
      n = n - 4;
      i = y;
    }
    y = i << 2;
    if (y != 0) {
      n = n - 2;
      i = y;
    }
    return n - ((i << 1) >>> 31);
  }

  /**
   * Returns the number of one-bits in the two's complement binary
   * representation of the specified {@code int} value.  This function is
   * sometimes referred to as the <i>population count</i>.
   *
   * @param i the value whose bits are to be counted
   * @return the number of one-bits in the two's complement binary representation of the specified
   * {@code int} value.
   * @since 1.5
   */
  public static int bitCount(int i) {
    // HD, Figure 5-2
    i = i - ((i >>> 1) & 0x55555555);
    i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
    i = (i + (i >>> 4)) & 0x0f0f0f0f;
    i = i + (i >>> 8);
    i = i + (i >>> 16);
    return i & 0x3f;
  }

  /**
   * Returns the value obtained by rotating the two's complement binary
   * representation of the specified {@code int} value left by the
   * specified number of bits.  (Bits shifted out of the left hand, or
   * high-order, side reenter on the right, or low-order.)
   *
   * <p>Note that left rotation with a negative distance is equivalent to
   * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
   * distance)}.  Note also that rotation by any multiple of 32 is a
   * no-op, so all but the last five bits of the rotation distance can be
   * ignored, even if the distance is negative: {@code rotateLeft(val,
   * distance) == rotateLeft(val, distance & 0x1F)}.
   *
   * @param i the value whose bits are to be rotated left
   * @param distance the number of bit positions to rotate left
   * @return the value obtained by rotating the two's complement binary representation of the
   * specified {@code int} value left by the specified number of bits.
   * @since 1.5
   */
  public static int rotateLeft(int i, int distance) {
    return (i << distance) | (i >>> -distance);
  }

  /**
   * Returns the value obtained by rotating the two's complement binary
   * representation of the specified {@code int} value right by the
   * specified number of bits.  (Bits shifted out of the right hand, or
   * low-order, side reenter on the left, or high-order.)
   *
   * <p>Note that right rotation with a negative distance is equivalent to
   * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
   * distance)}.  Note also that rotation by any multiple of 32 is a
   * no-op, so all but the last five bits of the rotation distance can be
   * ignored, even if the distance is negative: {@code rotateRight(val,
   * distance) == rotateRight(val, distance & 0x1F)}.
   *
   * @param i the value whose bits are to be rotated right
   * @param distance the number of bit positions to rotate right
   * @return the value obtained by rotating the two's complement binary representation of the
   * specified {@code int} value right by the specified number of bits.
   * @since 1.5
   */
  public static int rotateRight(int i, int distance) {
    return (i >>> distance) | (i << -distance);
  }

  /**
   * Returns the value obtained by reversing the order of the bits in the
   * two's complement binary representation of the specified {@code int}
   * value.
   *
   * @param i the value to be reversed
   * @return the value obtained by reversing order of the bits in the specified {@code int} value.
   * @since 1.5
   */
  public static int reverse(int i) {
    // HD, Figure 7-1
    i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
    i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
    i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
    i = (i << 24) | ((i & 0xff00) << 8) |
        ((i >>> 8) & 0xff00) | (i >>> 24);
    return i;
  }

  /**
   * Returns the signum function of the specified {@code int} value.  (The
   * return value is -1 if the specified value is negative; 0 if the
   * specified value is zero; and 1 if the specified value is positive.)
   *
   * @param i the value whose signum is to be computed
   * @return the signum function of the specified {@code int} value.
   * @since 1.5
   */
  public static int signum(int i) {
    // HD, Section 2-7
    return (i >> 31) | (-i >>> 31);
  }

  /**
   * Returns the value obtained by reversing the order of the bytes in the
   * two's complement representation of the specified {@code int} value.
   *
   * @param i the value whose bytes are to be reversed
   * @return the value obtained by reversing the bytes in the specified {@code int} value.
   * @since 1.5
   */
  public static int reverseBytes(int i) {
    return ((i >>> 24)) |
        ((i >> 8) & 0xFF00) |
        ((i << 8) & 0xFF0000) |
        ((i << 24));
  }

  /**
   * Adds two integers together as per the + operator.
   *
   * @param a the first operand
   * @param b the second operand
   * @return the sum of {@code a} and {@code b}
   * @see java.util.function.BinaryOperator
   * @since 1.8
   */
  public static int sum(int a, int b) {
    return a + b;
  }

  /**
   * Returns the greater of two {@code int} values
   * as if by calling {@link Math#max(int, int) Math.max}.
   *
   * @param a the first operand
   * @param b the second operand
   * @return the greater of {@code a} and {@code b}
   * @see java.util.function.BinaryOperator
   * @since 1.8
   */
  public static int max(int a, int b) {
    return Math.max(a, b);
  }

  /**
   * Returns the smaller of two {@code int} values
   * as if by calling {@link Math#min(int, int) Math.min}.
   *
   * @param a the first operand
   * @param b the second operand
   * @return the smaller of {@code a} and {@code b}
   * @see java.util.function.BinaryOperator
   * @since 1.8
   */
  public static int min(int a, int b) {
    return Math.min(a, b);
  }

  /**
   * use serialVersionUID from JDK 1.0.2 for interoperability
   */
  @Native
  private static final long serialVersionUID = 1360826667806852920L;
}
